Lemma 6.48 (See [1]}.) 
 Referring to Notation REF ,
\(x_i &= \varphi _i \phi _i\frac{ \tau ^*_{i-1} (\theta ^*_{i-1}) \eta ^*_{d-i} (\theta ^*_i) }{ \tau ^*_i (\theta ^*_i) \eta ^*_{d-i+1}( \theta ^*_{i-1}) }&& (1 \le i \le d).\) 

